P-FEMs for hyperelastic anisotropic nearly incompressible materials under finite deformations with applications to arteries simulation

The displacement-formulation of p-FEMs is extended to nearly incompressible hyper-elastic anisotropic materials under finite deformations in a three-dimensional setting. To demonstrate the efficiency and accuracy of the formulation, we derive analytical solutions that serve for the verification of the p-FE results. The locking-free properties at the limit of incompressibility, the high convergence rates and the robustness with respect to large aspect ratios of the p-FEs are demonstrated by numerical experiments and compared (in terms of degrees of freedom and CPU times) to equivalent classical formulations using h-FEMs. p-FEMs are then exploited to investigate artery-like structures having complex constitutive models and particularly the influence of slight allowable compressibility (of orders of several percents) on the stress levels.